Question: The following line passes through point $(-6, -9)$ : $y = \dfrac{7}{16} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(-6, -9)$ into the equation gives: $-9 = \dfrac{7}{16} \cdot -6 + b$ $-9 = -\dfrac{21}{8} + b$ $b = -9 + \dfrac{21}{8}$ $b = -\dfrac{51}{8}$ Plugging in $-\dfrac{51}{8}$ for $b$, we get $y = \dfrac{7}{16} x - \dfrac{51}{8}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-6, -9)$